Advertisement

Mid-Term Home Health Care Planning Problem with Flexible Departing Way for Caregivers

  • Wenheng Liu
  • Mahjoub Dridi
  • Hongying FeiEmail author
  • Amir Hajjam El Hassani
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume SCI 871)

Abstract

Home Health Care (HHC) centers aim to deliver health care service to patients at their domiciles to help them recover in a convenient environment. Staffs planning in HHC centers have always been a challenging task because this issue not only just dispatches suitable caregivers to serve patients with considering many peculiar constraints, such as, time window of patients, qualification and mandatory break of caregivers, but also seeks optimal solution to achieve its objective, which is often taken to equivalent to minimize total operational cost, or to maximize satisfaction of patients or caregivers. This chapter formulates a mixed integer programming model for mid-term HHC planning problem, which aims at minimizing the total operational cost of HHC centers. We define the real-life constraints as follows: patients need to be visited once or for several times during the planning horizon by capable caregivers; patients must be served in their time window; each patient has specific preferences to caregivers for some personal reasons (e.g. gender); caregivers work in their contract working time with no more than daily maximum working time; a lunch break happens only if caregivers start to work before the lunch start time and finish working after the lunch end time. Specially, in real life, caregivers can use their own cars or rent cars from HHC center to complete their service tasks, and thus, this chapter firstly concerns a flexible departing way for caregivers, which means that each caregiver can either start working from their domiciles or from HHC center according to the transportation mode chosen though they must end their work at HHC center. We call this way of providing service by caregivers as Center and Domicile to Center (CDC). In addition, in order to discuss the relationship between caregivers’ geographical areas and optimal results, we put forward the other two scenarios, (1) each caregiver must only depart from and return to the HHC center, and this case is named as Center to Center (CC); (2) each caregiver departs from their own domicile and returns to HHC center, this scenario is named as Domicile to Center (DC). As the departing ways for caregivers keep the same in these two scenarios, they can be called fixed departing ways. All these models are solved by a commercial programming solver Gurobi through the two group modified classic Periodic Vehicle Routing Problem with Time Windows (PVRPTW) benchmark instances and the other two group instances generated randomly. In total, 21 instances with up to 12 caregivers, 20 patients and 47 demands during the planning horizon. Experimental results show that the model CDC is the best model as it can find optimal solution for 90% instances, and solve the problem with least computational time for 40% instances. Model CC gets the worst results with no optimal solution can be obtained for all instances. This work will help HHC centers planners make proper decision through managing the depart way of caregivers that satisfy the real life constraints, minimize the total operational cost as well as find the optimal solution efficiency.

Notes

Acknowledgments

The first author thanks the China Scholarship Council for financial support gratefully. (Contract N.201801810101).

References

  1. 1.
    Sahoo, A.K., S. Mallik, C. Pradhan, B.S.P. Mishra, R.K. Barik, and H. Das. 2019. Intelligence-based health recommendation system using big data analytics. In Big data analytics for intelligent healthcare management, 227–246. Academic Press.Google Scholar
  2. 2.
    Emiliano, W., J. Telhada, and M. Carvalho. 2017. Home health care logistics planning: A review and framework. Procedia Manufacturing. 13: 948–955.CrossRefGoogle Scholar
  3. 3.
    Harris-Kojetin L., M. Sengupta, E. Park-Lee, and R. Valverde. 2013. Long-term care services in the United States: 2013 overview. National Center for Health Statistics Vital Health Stat, 3–37.Google Scholar
  4. 4.
    Morris, M. 2016. Global health care outlook: Battling costs while improving care.Google Scholar
  5. 5.
    Genet, N., W. Boerma, M. Kroneman, A. Hutchinson, and R.B. Saltman. 2012. Home care across Europe—current structure and future challenges. European observatory on health systems and policies. Oslo, Norway: World Health Organization.Google Scholar
  6. 6.
    Mankowska, D., F. Meisel, and C. Bierwirth. 2013. The home health care routing and scheduling problem with interdependent services. Health Care Management Science 17: 15–30.CrossRefGoogle Scholar
  7. 7.
    Begur, S., D. Miller, and J. Weaver. 1997. An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces 27: 35–48.CrossRefGoogle Scholar
  8. 8.
    Cheng, E., and J.L. Rich. 1998. A home health care routing and scheduling problem. Department of CAAM, Rice University, Houston Texas.Google Scholar
  9. 9.
    Bektas, T. 2006. The multiple traveling salesman problem: An overview of formulations and solution procedures. Omega 34: 209–219.CrossRefGoogle Scholar
  10. 10.
    Akjiratikarl, C., P. Yenradee, and P. Drake. 2007. PSO-based algorithm for home care worker scheduling in the UK. Computers & Industrial Engineering 53: 559–583.CrossRefGoogle Scholar
  11. 11.
    Kergosien Y., C. Lenté, and J-C. Billaut. 2009. Home health care problem: An extended multiple traveling salesman problem. In 4th multidisciplinary international conference on scheduling: Theory and applications, Dublin, Ireland.Google Scholar
  12. 12.
    Trautsamwieser, A., M. Gronalt, and P. Hirsch. 2011. Securing home health care in times of natural disasters. OR Spectrum 33: 787–813.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Eveborn, P., P. Flisberg, and M. Rönnqvist. 2006. Laps Care—an operational system for staff planning of home care. European Journal of Operational Research 171: 962–976.CrossRefGoogle Scholar
  14. 14.
    Nickel, S., M. Schröder, and J. Steeg. 2012. Mid-term and short-term planning support for home health care services. European Journal of Operational Research 219: 574–587.CrossRefGoogle Scholar
  15. 15.
    Rodriguez, C., T. Garaix, X. Xie, and V. Augusto. 2015. Staff dimensioning in homecare services with uncertain demands. International Journal of Production Research 53: 7396–7410.CrossRefGoogle Scholar
  16. 16.
    Decerle, J., O. Grunder, A. Hajjam El Hassani, and O. Barakat. 2019. A memetic algorithm for multi-objective optimization of the home health care problem. Swarm and Evolutionary Computation 44: 712–727.CrossRefGoogle Scholar
  17. 17.
    Wirnitzer, J., I. Heckmann, A. Meyer, and S. Nickel. 2016. Patient-based nurse rostering in home care. Operations Research for Health Care 8: 91–102.CrossRefGoogle Scholar
  18. 18.
    Braekers, K., R. Hartl, S. Parragh, and F. Tricoire. 2016. A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience. European Journal of Operational Research 248: 428–443.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Xiao, L., M. Dridi, and A. El Hassani. 2018. Mathematical model for the home health care scheduling and routing problem with flexible lunch break requirements. IFAC-PapersOnLine 51: 334–339.CrossRefGoogle Scholar
  20. 20.
    Bachouch, R., A. Guinet, and S. Hajri-Gabouj. 2011. A decision-making tool for home health care nurses’ planning. Supply Chain Forum: An International Journal 12: 14–20.CrossRefGoogle Scholar
  21. 21.
    Liu, R., B. Yuan, and Z. Jiang. 2016. Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements. International Journal of Production Research 55: 558–575.CrossRefGoogle Scholar
  22. 22.
    Chen, X., B. Thomas, and M. Hewitt. 2017. Multi-period technician scheduling with experience-based service times and stochastic customers. Computers & Operations Research 82: 1–14.MathSciNetCrossRefGoogle Scholar
  23. 23.
    Moussavi, S., M. Mahdjoub, and O. Grunder. 2019. A matheuristic approach to the integration of worker assignment and vehicle routing problems: Application to home healthcare scheduling. Expert Systems with Applications 125: 317–332.CrossRefGoogle Scholar
  24. 24.
    Bennett, A., and A. Erera. 2011. Dynamic periodic fixed appointment scheduling for home health. IIE Transactions on Healthcare Systems Engineering 1: 6–19.CrossRefGoogle Scholar
  25. 25.
    Maya Duque, P., M. Castro, K. Sörensen, and P. Goos. 2015. Home care service planning. The case of Landelijke Thuiszorg. European Journal of Operational Research 243: 292–301.CrossRefGoogle Scholar
  26. 26.
    Liu, R., X. Xie, and T. Garaix. 2014. Hybridization of tabu search with feasible and infeasible local searches for periodic home health care logistics. Omega 47: 17–32.CrossRefGoogle Scholar
  27. 27.
    Bard, J., Y. Shao, and A. Jarrah. 2013. A sequential GRASP for the therapist routing and scheduling problem. Journal of Scheduling 17: 109–133.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Hewitt, M., M. Nowak, and N. Nataraj. 2016. Planning Strategies for Home Health Care Delivery. Asia-Pacific Journal of Operational Research 33: 1650041.MathSciNetCrossRefGoogle Scholar
  29. 29.
    Hiermann, G., M. Prandtstetter, A. Rendl, J. Puchinger, and G. Raidl. 2013. Metaheuristics for solving a multimodal home-healthcare scheduling problem. Central European Journal of Operations Research 23: 89–113.MathSciNetCrossRefGoogle Scholar
  30. 30.
    Redjem, R., and E. Marcon. 2015. Operations management in the home care services: A heuristic for the caregivers’ routing problem. Flexible Services and Manufacturing Journal 28: 280–303.CrossRefGoogle Scholar
  31. 31.
    Trautsamwieser, A., and P. Hirsch. 2014. A branch-price-and-cut approach for solving the medium-term home health care planning problem. Networks 64: 143–159.CrossRefGoogle Scholar
  32. 32.
    Ikegami, A., and A. Uno. 2007. Bounds for staff size in home help staff scheduling. In The 50th Anniversary of the Operations Research Society of Japan 4: 563–575.Google Scholar
  33. 33.
    Fikar, C., and P. Hirsch. 2017. Home health care routing and scheduling: A review. Computers & Operations Research 77: 86–95.MathSciNetCrossRefGoogle Scholar
  34. 34.
    Cissé, M., S. Yalçındağ, Y. Kergosien, E. Şahin, C. Lenté, and A. Matta. 2017. OR problems related to Home Health Care: A review of relevant routing and scheduling problems. Operations Research for Health Care 13: 1–22.CrossRefGoogle Scholar
  35. 35.
    Kara, I., G. Laporte, and T. Bektas. 2004. A note on the lifted Miller–Tucker–Zemlin subtour elimination constraints for the capacitated vehicle routing problem. European Journal of Operational Research 158: 793–795.MathSciNetCrossRefGoogle Scholar
  36. 36.
    Cordeau, J., G. Laporte, and A. Mercier. 2001. A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society 52: 928–936.CrossRefGoogle Scholar
  37. 37.
    Shi, Y., T. Boudouh, O. Grunder, and D. Wang. 2018. Modeling and solving simultaneous delivery and pick-up problem with stochastic travel and service times in home health care. Expert Systems with Applications 102: 218–233.CrossRefGoogle Scholar
  38. 38.
    Shi, Y., T. Boudouh, and O. Grunder. 2019. A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times. Transportation Research Part E: Logistics and Transportation Review 128: 52–95.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Wenheng Liu
    • 1
  • Mahjoub Dridi
    • 1
  • Hongying Fei
    • 2
    Email author
  • Amir Hajjam El Hassani
    • 1
  1. 1.Nanomedicine LabUniversity Bourgogne Franche-Comté, UTBMBelfortFrance
  2. 2.School of ManagementShanghai UniversityBaoshan District, ShanghaiChina

Personalised recommendations